# If the function f(x) = (3x-c)/(ax+2) is a constant function, what is the value of a*c ?

Jul 12, 2016

$a c = - 6$

#### Explanation:

$f \left(x\right)$ being a constant function it will have same value for all real values of x.

So

$f \left(0\right) = f \left(1\right)$

$\implies \frac{3 \cdot 0 - c}{a \cdot 0 + 2} = \frac{3 \cdot 1 - c}{a \cdot 1 + 2}$

$- c \left(a + 2\right) = 2 \cdot \left(3 - c\right)$

$\implies - a c - 2 c = 6 - 2 c$

$\implies a c = - 6$

Otherwise differentiating the function $f \left(x\right)$ w.r.to x and equating $f ' \left(x\right) = 0$ we can get the same result.